How to take the derivative using the product rule with sine

The video tutorial explains the process of finding derivatives, focusing on the constant rule and product rule. It begins with an introduction to derivatives, followed by a detailed explanation of the product rule. The instructor sets up the derivative calculation and then performs and simplifies the calculations, ensuring students understand each step.

What is the significance of the negative sign in the derivative of cosine of X?

How does the teacher simplify the expression after finding the derivative?